The paper analyzes the role of governmental debt in an overlapping generations economy with stochastic production and capital accumulation. In the absence of taxation, equilibria with positive debt generically converge to debtless equilibria which are dynamically inefficient. It is shown that this may be overcome by a tax on labor income which stabilizes the level of debt against deviations from some reference value that identifies a stable path of the underlying dynamical system. A modified golden rule criterion is formulated which measures consumer welfare at the stabilized equilibrium. Based on this criterion, the welfare effects of different levels of debt and different interest policies are investigated with the help of numerical simulations.